$n+S(n)=2014\Rightarrow n<2014 \Rightarrow $ n có 4 chữ số
Đặt $n=\overline{abcd},(a\neq0)$
Do $n<2014 \Rightarrow a\leq2$
TH2:$a=2$,ta có:$\overline{2bcd}+2+b+c+d=2014 \Rightarrow \overline{bcd}+b+c+d=12 $
$\Rightarrow b=0;c=1;d=0,5(loại)$
TH1:$a=1$,ta có:$\overline{1bcd}+1+b+c+d=2014\Rightarrow \overline{bcd}+b+c+d=1013$
Do $b+c+d\leq27 \Rightarrow \overline{bcd}\geq 986 \Rightarrow b=9$
$\Rightarrow \overline{9cd}+9+c+d=1013\Rightarrow \overline{cd}+c+d=104\Rightarrow \overline{cd}\geq86$
$\Rightarrow$c=8 hoặc c=9
*)$c=8\Rightarrow d=8$
*)$c=9\Rightarrow d=2,5(loại)$
vậy $n=1988$